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Computer simulation of a twisted nanotube buckling

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Abstract

We develop procedures for solving the problems of dynamic nanostructure deformation and buckling numerically. The procedures are based on discretization with respect to time of the nonlinear equations of molecular mechanics whose matrices and vectors are determined using the Morse potential for the central forces of interaction between atoms and fictitious truss elements accounting for the variations of the angle between atomic bonds. To determine the critical values of deformation parameters and the shapes of buckling nanostructures we use a stability loss criterion for solutions to nonlinear ordinary differential equations on a finite time interval. We implemented our procedures in the PIONER code, using which we solve the problem of a twisted nanotube buckling in the conditions of a quasistatic deformation. To determine the postcritical equilibrium modes we solve the same problem in a dynamic formulation. We show that the modes of equilibrium configurations of the nanotube in the initial postcritical deformation correspond to a buckling mode obtained both at the bifurcation point of quasistatic solutions and at the quasibifurcation point of dynamic solutions.

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, pr. Akad. Lavrent’eva 15, Novosibirsk, 630090, Russia

    B. D. Annin & S. N. Korobeynikov

  2. Institute of Geology and Mineralogy, pr. Akad. Koptyuga 3, Novosibirsk, 630090, Russia

    A. V. Babichev

Authors
  1. B. D. Annin
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  2. S. N. Korobeynikov
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  3. A. V. Babichev
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Correspondence to S. N. Korobeynikov.

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Original Russian Text © B.D. Annin, S.N. Korobeynikov, A.V. Babichev, 2008, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2008, Vol. XI, No. 1, pp. 3–22.

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Annin, B.D., Korobeynikov, S.N. & Babichev, A.V. Computer simulation of a twisted nanotube buckling. J. Appl. Ind. Math. 3, 318–333 (2009). https://doi.org/10.1134/S1990478909030028

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